Integration problem

  • Thread starter crm08
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  • #1
crm08
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Homework Statement



[tex]\int(\frac{x}{\sqrt{1-x^{2}}})dx[/tex]

Homework Equations





The Attempt at a Solution



My calculator tells me that the answer should be -sqrt(1-x^2) but if I pick u = sqrt(1-x^2), then dx = (sqrt(1-x^2)*du)/x, which leaves me with -integral((sqrt(1-x^2)/u)du), the problem I am having is getting rid of the "ln(u)" in my final answer, any suggestions?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,223
31
If u^2=1-x^2
2u du =-2x dx => - u du = x dx

Now you'd just get

[tex]\frac{-u}{u} du[/tex]
 
  • #3
crm08
28
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ok got it, thank you
 
  • #4
36,313
8,282
If u^2=1-x^2
2u du =-2x dx => - u du = x dx

Now you'd just get

[tex]\frac{-u}{u} du[/tex]
Another substitution that works is u = 1 - x^2, du = -2xdx.
The integrand then becomes -(1/2)du/u^(1/2), which is also an easy one to integrate.
 

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